CAPACITORS 

Capacitance

If Q is the charge given to a conductor and V is the potential to which it is raised by this amount of charge, then it is found that Q ∝V. Or Q = CV, where C is a constant called capacitance of the conductor.
    C =  Q ⁄ V
For parallel plate capacitor C = 1851_capacitance.JPG

i.e. the capacitance depends only on geometrical factors namely, the plate area and plate separation.
Spherical Capacitor

450_capacitor.JPG

Isolated Capacitor
An isolated sphere can be thought of as a capacitor where other plate is at infinity.
    R1 = R     and R2 = ∞

1426_capacitors.JPG

• Combination of Capacitors

Series Combination: In series combination, each capacitors has equal charge for any value of capacitance. Equivalent capacitance C is given by

 

928_diagram.JPG

Parallel Combination:

In parallel combination the potential differences of the capacitor connected in parallel are equal for any of capacitor.  Equivalent capacitance is given by
    C = C1 + C2 + C3

 1518_capacitance.JPG

Example 10.    In the above circuit, find the potential difference across AB.

 1279_figure.JPG

Solution:    Let us mark the capacitors as 1, 2, 3 and 4 for identifications. As is clear, 3 and 4 are in series, and they are in parallel with 2. Then 2, 3, 4 combine is in series with 1.

 

240_capacitor.JPG

Dielectric
Substances having polar atoms/molecules intrinsically or being polarized are called dielectrics.
Polar Dielectric
Substances which have polar atoms/molecules intrinsically but are randomly arranged. On application of external electric field they get polarized parallel to the external electric field.

Net electric field inside dielectric.

      207_capacitor.JPG

787_capacitor.JPG

Capacitance of a parallel plate capacitor having dielectric slabs in series.

 434_capacitor.JPG

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